Chapter 8.6, Problem 14PPS

To determine

To factor: The polynomial $n^2-2n-35$ . Confirm your answer using a graphing calculator.

Answer to Problem 14PPS

  $\left(n-7\right)\left(n+5\right)$

Explanation of Solution

Given:

  $n^2-2n-35$

Calculation:

The given polynomial is $n^2-2n-35$

Rewrite the middle term as $-2n=-7n+5n$ . So, the polynomial becomes

  $n^2-7n+5n-35$

Make group as shown below

  $\left(n^2-7n\right)+\left(5n-35\right)$

Factor out the GCF from each of the group

  $n\left(n-7\right)+5\left(n-7\right)$

Finally, factored out the common factor

  $\left(n-7\right)\left(n+5\right)$

Therefore, the factored form of the given polynomial is $\left(n-7\right)\left(n+5\right)$

Now, using a graphing calculator, the factor of the polynomial is given by

  $\left(n-7\right)\left(n+5\right)$

So, the answer is verified.